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Let A(t) = 3- 2t^2 + 4^t. Find A(2) - A(1).

 

The function f satisfies f(sqrt(x+1)) = 1/x for all $x >= -1, x does not equal 0. Find f(2).

 

Thanks :D

WhichWitchIsWhich  Oct 29, 2017

Best Answer 

 #1
avatar+7096 
+1

A(t)  =  3 - 2t2 + 4t

 

A(2)  =  3 - 2(2)2 + 42

 

A(1)  =  3 - 2(1)2 + 41

 

A(2) - A(1)  =  [ 3 - 2(2)2 + 42 ] - [ 3 - 2(1)2 + 41 ]

 

A(2) - A(1)  =  [ 3 - 2(4) + 16 ] - [ 3 - 2(1) + 4 ]

A(2) - A(1)  =  [ 3 - 8 + 16 ] - [ 3 - 2 + 4 ]

A(2) - A(1)  =  [ 11 ] - [ 5 ]

A(2) - A(1)  =    6

 

----------

 

f( √[x + 1] )  =  1/x      for  x ≥ -1  and  x ≠ 0  

 

We want to find  f(2)  , so we need an x value that makes

 

√[ x + 1]  =  2      square both sides

x + 1  =  4           subtract  1  from both sides

x  =  3                 This is a valid  x  to plug in.

 

So....

 

f( √[3 + 1] )  =  1/3

f( 2 )  =  1/3                 smiley

hectictar  Oct 29, 2017
 #1
avatar+7096 
+1
Best Answer

A(t)  =  3 - 2t2 + 4t

 

A(2)  =  3 - 2(2)2 + 42

 

A(1)  =  3 - 2(1)2 + 41

 

A(2) - A(1)  =  [ 3 - 2(2)2 + 42 ] - [ 3 - 2(1)2 + 41 ]

 

A(2) - A(1)  =  [ 3 - 2(4) + 16 ] - [ 3 - 2(1) + 4 ]

A(2) - A(1)  =  [ 3 - 8 + 16 ] - [ 3 - 2 + 4 ]

A(2) - A(1)  =  [ 11 ] - [ 5 ]

A(2) - A(1)  =    6

 

----------

 

f( √[x + 1] )  =  1/x      for  x ≥ -1  and  x ≠ 0  

 

We want to find  f(2)  , so we need an x value that makes

 

√[ x + 1]  =  2      square both sides

x + 1  =  4           subtract  1  from both sides

x  =  3                 This is a valid  x  to plug in.

 

So....

 

f( √[3 + 1] )  =  1/3

f( 2 )  =  1/3                 smiley

hectictar  Oct 29, 2017

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